Mathematics Stack Exchange
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Questions tagged [permutations]

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

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String Permutation

If we have the string ab, would abab be a permutation of ab? It seems that a permutation is a rearrangement of things but only within the things in our set. In this example, that set is ab.
A user
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In how many ways can the letters of the word 'arrange' be arranged if the two r's and the two a's do not occur together?

In how many ways can the letters of the word 'arrange' be arranged if the two r's and the two a's do not occur together?
kenil shah
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Why do we divide the number of repetitive alphabets rather than subract during permutation?

The question is how many ways the word INDIA can be re-written. I N D I A There are 5 letters in this word. The letter I is repeated twice, and this number doesn't make any sense if there positions are interchanged. So,basically the number of…
dexterous
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The number of permutations with a distance condition

How can I think about this question: I have a string of As and Bs and I want the number of permutations such that the distance between two Bs is at least 2 for n = 3, the number of valid strings is 4 BAA AAB ABA AAA for n = 6, AABAAB is valid…
stupid
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The permutation $\lambda_g \quad : \quad G \longmapsto G \quad : \quad x \mapsto gx$

Let $G$ be a group containing $2k$ lements where $k$ is odd. Let $g \in G$ of order $2$ and define $$ \lambda_g \quad : \quad G \longmapsto G \quad : \quad x \mapsto gx $$ I had to show that $\lambda_g$ is an odd permutation in $S(G)$. I know that…
Koenraad van Duin
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permutation game labels

A computer game has five difficulty levels. In each level you can choose among four different scenarios except for the first level, where you can choose among three scenarios only. How many different games are possible? My answer is: $3\times 4…
user52950
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Permutation of objects selected from a group

I'm having trouble with this question: How many numbers greater than 300 can be formed from the figures 4, 3, 2 and 1 if each figure can be used no more than once in each number and all the figures need not be used each time? Here is my approach.…
hohner
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How many even numbers greater than 50 000 can be formed from specified digits without repeat?

The digits are 3,4,5,6,7,0 My working is as follows: I realize that you would need to start with either 5,6 or 7. From there you have 5 digits to re-arrange, but the permutation would have to end in an even number. Starting with 5 you would end…
Graeme Harris
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Finding String permuatations

Given a string of characters(a-z) ,find subsequence such that every character is strictly greater than all previous characters in that subsequence. Example if S=abc then there are 7 subsequences which follow the above constraint. These are…
savvi singh
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How many permutations of all the letters in the word ARMADILLO begin with letter A?

I know that there are 9 total letters and there are three A`s and two L`s. Is the answer just $9!/(3!*2!)$? Thanks for any help.
ToxicTechnetium
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How many configurations

If I have twelve objects, each of which can be in one of three states (say on, off, on/off), how many ways can the group of twelve be configured -- by changing the state of each object?
user156300
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A common combinatorics problem

Suppose the final result of a football match is 5−4, the home team winning. If the home team scored first and kept the lead until the end, in how many different orders could the goals have been scored? I have seen this problem at many places but I…
idpd15
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Discrete Math Permutations help

Is it true that there are $5!$ possible sequences of five specific names? Wouldn't this be true since there are $5!$ arrangements?
user149068
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Find the number of $4$-digit numbers that can be formed using $1,2,3,4,5$ if no digit is repeated. How many of these will be even?

I'm unable to solve this question. Please help. I have no idea. The given answers are $120$ and $48$. I got $120$ but not $48$. This is how I got $120$. No repetition allowed, so $5\times4\times3\times2=120$ ways.
CHETAN
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In how many subsets of {1,2,3 ... 9,10} there are odd number of objects from {1,2,3,4,5} and even number of objects from {6,7,8,9,10}?

In how many subsets of {1,2,3 ... 9,10} there are odd number/s of objects from {1,2,3,4,5} and even numbers of objects from {6,7,8,9,10} ? The answer I remember is 2^4 . 2^4 ( But It may not be correct )
combine
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